The influences of supersaturation on LPE growth of GaN single crystals using the Na flux method

The dependency of LPE growth rate and dislocation density on supersaturation in the growth of GaN single crystals in the Na flux was investigated. When the growth rate was low during the growth of GaN at a small value of supersaturation, the dislocation density was much lower compared with that of a substrate grown by the Metal Organic Chemical Vapor Deposition method (MOCVD). In contrast, when the growth rate of GaN was high at a large value of supersaturation, the crystal was hopper including a large number of dislocations. The relationship between the growth conditions and the crystal color in GaN single crystals grown in Na flux was also investigated. When at 800 °C the nitrogen concentration in Na–Ga melt was low, the grown crystals were always tinted black. When the nitrogen concentration at 850 °C was high, transparent crystals could be grown.     

Crystal structure of cyanocalix[4]arene methyl ether

The title compound has been prepared by the addition of bromocalix[4]arene methyl ether to CuCN in N-methylpyrrolidone. The crystals belong to the monoclinic space groupP2₁/n witha=13.591(3),b=24.778(5),c=11.057(3)Å,=93.58(2)°, andD _c=1.09 g cm^–3 forZ=4. Refinement based on 1118 observed reflections led to a finalR value of 0.085. The molecule exhibits the partial cone conformation.     

Functional integral representations of the Pauli-Fierz model with spin 1/2

A Feynman-Kac-type formula for a Lévy and an infinite-dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of e−tHPF generated by the Pauli-Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics is constructed. When no external potential is applied HPF turns translation-invariant and it is decomposed as a direct integral . The functional integral representation of e−tHPF(P) is also given. Although all these Hamiltonians include spin, nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions. As an application of the functional integral representations energy comparison inequalities are derived.     

Error Correcting Sequence and Projective De Bruijn Graph

Let X be a finite set of q elements, and n, K, d be integers. A subset C ⊂ X ⁿ is an (n, K, d) error-correcting code, if #(C) = K and its minimum distance is d. We define an (n, K, d) error-correcting sequence over X as a periodic sequence {a _i } _i=0,1,... (a _i ∈ X) with period K, such that the set of all consecutive n-tuples of this sequence form an (n, K, d) error-correcting code over X. Under a moderate conjecture on the existence of some type of primitive polynomials, we prove that there is a error correcting sequence, such that its code-set is the q-ary Hamming code with 0 removed, for q > 2 being a prime power. For the case q = 2, under a similar conjecture, we prove that there is a error-correcting sequence, such that its code-set supplemented with 0 is the subset of the binary Hamming code [2 ^m  − 1, 2 ^m  − 1 − m, 3] obtained by requiring one specified coordinate being 0. Received: October 27, 2005. Final Version received: December 31, 2007     

Donor-acceptor distance-dependence of photoinduced electron-transfer rate in flavoproteins

Ultrafast fluorescence quenching of flavin in flavodoxin from Megasphaera elsdenii was investigated by means of a fluorescence up-conversion method. Fluorescence lifetimes of flavodoxin from M. elsdenii were estimated to be tau(1) approximately 165 fs (0.97%) and tau(2) approximately 10 ps (0.03%). Correlation of photoinduced electron-transfer rates (k(ET)) with averaged distances (D(av)) between isoalloxazine and nearby tryptophan or tyrosine was examined and obtained an empirical equation of ln k(ET) vs D(av) by means of a nonlinear least-squares method using reported data together with flavodoxin from M. elsdenii. The values of D(av) were calculated from X-ray structures of the flavoproteins. The ln k(ET) was approximately linear at D(av) shorter than 7 A. The model free empirical equation was expressed as ln k(ET) = 29.7 + (-0.327 D(av) + 2.84 x 10(-5))/(0.698 - D(av)(2)). We also analyzed the observed values of ln k(ET) with Marcus theory, but could not obtain reasonable results. Our analysis suggests that the average distance, rather than the shortest (edge to edge) distance or interplanar angles between the aromatics rings, is the key factor in the process of the photoinduced electron transfer in these flavoproteins.     

Multiple enzyme linked immunosorbent assay system on a capillary-assembled microchip integrating valving and immuno-reaction functions

Gastrodin is a bioactive constituent of rhizome in Gastrodia elata Blume (Orchidaceae) The aim of this study is to develop a rapid and sensitive liquid chromatographic method coupled to microdialysis sampling system to measure the unbound of gastrodin in rat blood, brain and bile. Microdialysis probes were simultaneously inserted into the jugular vein, brain striatum and bile duct of each anesthetized rat for sampling after the administration of gastrodin (100 or 300 mg kg⁻¹) through the femoral vein. Separation of unbound gastrodin from various biological fluids was applied to an RP-select B column (250 mm × 4.6 mm i.d., 5 μm). The mobile phase consisted of acetonitrile–50 mM potassium dihydrogen phosphate buffer–triethylamine (5:95:0.1, v/v/v, adjusted to pH 2.5 with orthophosphoric acid) with a flow rate of 1 mL min⁻¹. The UV detector wavelength was set at 221 nm. Fifteen minutes after the administration, the gastrodin reached the peak concentration in brain and bile. In addition, the results indicate that gastrodin penetrates the blood-brain barrier (BBB) and goes through hepatobiliary excretion.     

Remarks on a posteriori error estimation for finite element solutions

We utilize the classical hypercircle method and the lowest-order Raviart–Thomas H(div)$H(\mathrm{div})$ element to obtain a posteriori error estimates of the _P1$P_1$ finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods.     

N-long-chain monoacylated derivatives of 2,6-diaminopyridine with antiviral activity

N-Monoacyl-2,6-diaminopyridines (2a-c) and N,N'-diacyl-2,6-diaminopyridines (3a-c) were synthesized from 2,6-diaminopyridine by acylation with the corresponding acyl halide or by dehydration with the corresponding carboxylic acid using 1,3-dicyclohexylcarbodiimide (DCC). The antiviral activities of N-monoacyl- and N,N'-diacyl-2,6-diaminopyridines (2a-c and 3a-c) were estimated using plaque reduction assay with HSV-1. All N-monoacyl derivatives (2a-c) showed significant anti-herpes simplex virus (HSV)-1 activity (EC(50) = 15.3-18.5 microg/ml). The CC(50) values of 2a-c measured using Vero cells ranged at 37.5-50.0 microg/ml. These compounds showed no significant antibacterial activities with Escherichia coli or Staphylococcus aureus even at a concentration of 1 mg/ml. The N,N'-diacyl derivatives (3a-c) showed no significant anti-HSV-1 activity.     

Unidirectional crystallization of charged colloidal silica due to the diffusion of a base

Dilute aqueous dispersions of charged colloidal silica (particle volume fraction = approximately 0.03-0.04, particle diameter = 110 nm) exhibit unidirectional crystal growth due to the diffusion of a weak base, pyridine (Py). Similar diffusion-crystallization is enabled by a salt of a weak acid and a strong base, sodium hydrogen carbonate (NaHCO3). The resulting crystals consist of columnar (or cubic) crystal grains with a maximum height of a few centimeters and a maximum width of 1 cm. The crystal growth process is attributed to a combination of (i) the diffusion of Py or NaHCO3 accompanied by a charging reaction of the silica particles and (ii) the charge-induced crystallization of the silica colloids. Theoretical growth curves based on the reaction-diffusion model for the case of Py were in good agreement with the observed curves. We also report the immobilization of the resulting large crystals by using a polymer hydrogel matrix.